Description of the Prior Art
This invention relates to digital to analog converters in general and more particularly to an improved digital to analog resolver converter.
A digital signal consisting of n bits can be used to represent the magnitude of an angle in radians or degrees, with the least significant bit representing 360/2.sup.n .degree. or 2.pi./2.sup.n radians. To simplify the discussion of the invention, all values will be stated in degrees, since radians can easily be substituted for degrees.
The n-bit digital signal representing the magnitude of an angle can be described by the notation 2.sub.1 2.sub.2 . . . 2.sub.n. Throughout this disclosure, the most significant bit (2.sub.1) will be referred to as the first bit, the second most significant bit (2.sub.2) as the second bit, and so forth, down to the least significant (2.sub.n) or nth bit.
It is evident that the less significant bits of the digital input signal only represent the magnitude of the angle over a given range of angular values. For example, the sixth through nth bits represent a range of angular values from 0.degree. up to 11.25.degree..
The prior art includes devices capable of converting a digital signal representing the magnitude of an angle to an analog signal representing the magnitude of the angle. These devices use switching networks to control the output of R-2R resistance ladders and generate an analog signal proportional to the digital input signal.
Prior art devices also exist which generate analog resolver functions corresponding to digital inputs. One type of device utilizes a digital sensor and digital to analog converter to provide proportional error signal to a servo-mechanism control shaft which positions an electromechanical resolver device to generate an output. Resolver functions can also be generated by two ladder networks or a multiplexed single ladder. Some solid state devices use programmed memory devices ("look up tables") to convert a digital angle signal to digital sine and cosine signals to generate a resolver function. Other solid state devices convert digital angle values to analog tangent angle values utilizing non-linear resistance networks. The tangent angle values are related to the reference voltage in a manner similar to a resolver function output.
All of these devices have serious disadvantages. The use of servo-mechanisms for digital to resolver conversions entails substantial cost, size, weight, accuracy and life disadvantages. The two ladder method involves use of an additional ladder and creates problems in tracking accuracy of the two ladders when the temperature changes. The open multiplexed single ladder needs additional circuitry for the multiplex function, involves additional phase lag errors proportional to the ratio of the multiplex frequency to the carrier frequency, and creates variations in scale factor as a function of angle. Solid state digital angle to resolver converters with "look-up tables" use too many discrete parts to achieve acceptable accuracy. Digital angle to tangent angle conversion devices have difficulty in accurately approximating the tangent function with non-linear analog means.
Copending U.S. patent application Ser. No. 624,740 discloses a solid state digital angle converter utilizing a single ladder network. This resolver is similar to the instant invention in using the concept of dividing the sine and cosine functions into segments and making linear approximations to these segments. However, this resolver uses two precision resistors to simulate many of the segments while the instant invention uses only one precision resistor to simulate most of the segments. The use of the minimum number of precision resistors reduces cost, lessens the likelihood of error in approximating the sine and cosine function, and allows monotonicity between the approximating chord segments.